Computation of effective conductivity of multiphase stochastic medium by 3D finite difference resistivity modeling and inversion

2011 ◽  
Author(s):  
Xiaoping Wu ◽  
Jingjin Lu ◽  
Yong Yu
Keyword(s):  
Finite Difference ◽  
Effective Conductivity ◽  
Stochastic Medium ◽  
And Inversion ◽  
Resistivity Modeling

scholarly journals 3-D DC resistivity modeling and inversion using multi-resolution framework

2019 ◽  
Vol 2019 (1) ◽  
pp. 1-3
Author(s):  
Jingyu Gao ◽  
Maxim Smirnov ◽  
Maria Smirnova ◽  
Gary Egbert
Keyword(s):  
Dc Resistivity ◽  
And Inversion ◽  
Resistivity Modeling

Mimetic finite-difference coupled-domain solver for anisotropic media

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. T45-T59
Author(s):  
Harpreet Sethi ◽  
Jeffrey Shragge ◽  
Ilya Tsvankin
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Model Building ◽  
Fluid Layer ◽  
Anisotropic Media ◽  
Horizontal Displacement ◽  
Solid Boundary ◽  
Ocean Bottom ◽  
Solid Interface ◽  
And Inversion

Accurately modeling full-wavefield solutions at and near the seafloor is challenging for conventional single-domain elastic finite-difference (FD) methods. Because they treat the fluid layer as a solid with zero shear-wave velocity, the energy partitioning for body and surface waves at the seafloor is distorted. This results in incorrect fluid/solid boundary conditions, which has significant implications for imaging and inversion applications that use amplitude information for model building. To address these issues, here we use mimetic FD (MFD) operators to develop and test a numerical approach for accurately implementing the boundary conditions at a fluid/solid interface. Instead of employing a single “global” model domain, we partition the full grid into two subdomains that represent the acoustic and elastic (possibly anisotropic) media. A novel split-node approach based on one-sided MFD operators is introduced to distribute grid points at the fluid/solid interface and satisfy the wave equation and the boundary conditions. Numerical examples demonstrate that such MFD operators achieve stable implementation of the boundary conditions with the same (fourth) order of spatial accuracy as that inside the split-domain interiors. We compare the wavefields produced by the MFD scheme with those from a more computationally expensive spectral-element method to validate our algorithm. The modeling results help analyze the events associated with the fluid/solid (seafloor) interface and provide valuable insights into the horizontal displacement or velocity components (e.g., recorded in ocean-bottom-node data sets). The developed MFD approach can be efficiently used in elastic anisotropic imaging and inversion applications involving ocean-bottom seismic data.

Finite-difference modeling with adaptive variable-length spatial operators

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. T79-T89 ◽  
Author(s):  
Yang Liu ◽  
Mrinal K. Sen
Keyword(s):  
Finite Difference ◽  
Dispersion Analysis ◽  
Variable Length ◽  
Finite Difference Schemes ◽  
Low Velocity ◽  
Absorbing Boundary ◽  
Local Grid ◽  
Spatial Derivatives ◽  
Spatial Operators ◽  
And Inversion

Most finite-difference simulation algorithms use fixed-length spatial operators to compute spatial derivatives. The choice of length is dictated by computing cost, stability, and dispersion criteria that are satisfied globally. We propose finite-difference schemes with adaptive variable-length spatial operators to decrease computing costs significantly without reducing accuracy. These schemes adopt long operators in regions of low velocity and short operators in regions of high velocity. Two methods automatically determine variable operator lengths. Dispersion analysis, along with 1D and 2D modeling, demonstrates the validity and efficiency of our schemes. In addition, a hybrid absorbing boundary condition helps reduce unwanted reflections from model boundaries. Our scheme is more efficient than those based on variable-grid methods for modeling, migration, and inversion of models with complex velocity structures because the latter require local grid refinement, which usually increases memory requirements and computing costs.

A PRACTICAL APPROACH TO FINITE‐DIFFERENCE RESISTIVITY MODELING

Geophysics ◽  
1978 ◽  
Vol 43 (5) ◽  
pp. 930-942 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Finite Difference ◽  
Point Source ◽  
Potential Field ◽  
Line Source ◽  
Sparse Matrix ◽  
Analytical Data ◽  
Parallel Layer ◽  
The Matrix ◽  
The Given ◽  
Resistivity Modeling

Highly efficient finite‐difference resistivity modeling algorithms which yield accurate results are put forward. The given medium is discretized and divided into rectangular blocks by using a very coarse system of vertical and horizontal grid lines, whose distance from the source(s) increases logarithmically. Expressions are derived to compute the longitudinal conductance and transverse resistance associated with each of these blocks for a parallel‐layer medium followed by a generalized treatment to accommodate arbitrarily shaped structures. Since the values of Dar Zarrouk parameters are derived from the exact resistivity distribution of the given medium, fine features such as a thin but anomalously resistive bed which ordinarily would be missed entirely in coarse discretization can be taken into account. Further reduction in the size of the model is achieved by making use of a symmetry wherever possible. In most cases the computation of the potential field which involves the inversion of a small sparse matrix requires about 0.5 sec of computer time. Moreover, changes in geology affect neither the size nor the zero structure of the matrix. Therefore, when more than one model is to be computed, the factorization of the matrix can be done symbolically only once for all models, followed by numeric factorization for each individual model. The coarse grid algorithm was applied to a number of horizontally layered models involving a point source. The results obtained for each model were in excellent agreement with the corresponding analytical data. Finite‐difference investigation of the potential field for two‐dimensional structures and a line source dipole indicates that as long as one is interested only in the evaluation of the Schlumberger‐type apparent resistivity curves, the line‐source results may be a much better approximation to the corresponding point‐source data than is commonly believed.

scholarly journals A hybrid finite-difference and integral-equation method for modeling and inversion of marine controlled-source electromagnetic data

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. E323-E336 ◽  
Author(s):  
Daeung Yoon ◽  
Michael S. Zhdanov ◽  
Johan Mattsson ◽  
Hongzhu Cai ◽  
Alexander Gribenko
Keyword(s):  
Integral Equation ◽  
Finite Difference ◽  
Electric Fields ◽  
Integral Equation Method ◽  
Numerical Differentiation ◽  
Forward Modeling ◽  
Staggered Grid ◽  
3D Inversion ◽  
Controlled Source ◽  
And Inversion

One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finite-difference (FD) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell’s equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields at the receivers are calculated using the IE method with the corresponding Green’s tensor for the background conductivity model. This approach makes it possible to compute the fields at the receivers accurately without the need of very fine FD discretization in the vicinity of the receivers and sources and without the need for numerical differentiation and interpolation. We have also developed an algorithm for 3D inversion based on the hybrid FD-IE method. In the case of the marine CSEM problem with multiple transmitters and receivers, the forward modeling and the Fréchet derivative calculations are very time consuming and require using large memory to store the intermediate results. To overcome those problems, we have applied the moving sensitivity domain approach to our inversion. A case study for the 3D inversion of towed streamer EM data collected by PGS over the Troll field in the North Sea demonstrated the effectiveness of the developed hybrid method.

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